4.49/1.98	YES
4.69/1.99	proof of /export/starexec/sandbox/benchmark/theBenchmark.c
4.69/1.99	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.69/1.99	
4.69/1.99	
4.69/1.99	Termination of the given C Problem could be proven:
4.69/1.99	
4.69/1.99	(0) C Problem
4.69/1.99	(1) CToIRSProof [EQUIVALENT, 0 ms]
4.69/1.99	(2) IntTRS
4.69/1.99	(3) TerminationGraphProcessor [SOUND, 27 ms]
4.69/1.99	(4) IntTRS
4.69/1.99	(5) IntTRSCompressionProof [EQUIVALENT, 1 ms]
4.69/1.99	(6) IntTRS
4.69/1.99	(7) IntTRSUnneededArgumentFilterProof [EQUIVALENT, 0 ms]
4.69/1.99	(8) IntTRS
4.69/1.99	(9) PolynomialOrderProcessor [EQUIVALENT, 1 ms]
4.69/1.99	(10) YES
4.69/1.99	
4.69/1.99	
4.69/1.99	----------------------------------------
4.69/1.99	
4.69/1.99	(0)
4.69/1.99	Obligation:
4.69/1.99	c file /export/starexec/sandbox/benchmark/theBenchmark.c
4.69/1.99	----------------------------------------
4.69/1.99	
4.69/1.99	(1) CToIRSProof (EQUIVALENT)
4.69/1.99	Parsed C Integer Program as IRS.
4.69/1.99	----------------------------------------
4.69/1.99	
4.69/1.99	(2)
4.69/1.99	Obligation:
4.69/1.99	Rules:
4.69/1.99	f1(i, n) -> f2(i, x_1) :|: TRUE
4.69/1.99	f2(x, x1) -> f3(arith, x1) :|: TRUE && arith = x1 - 1
4.69/1.99	f4(x10, x11) -> f5(x12, x11) :|: TRUE && x12 = x10 - 1
4.69/1.99	f3(x4, x5) -> f4(x4, x5) :|: x4 > 1
4.69/1.99	f5(x6, x7) -> f3(x6, x7) :|: TRUE
4.69/1.99	f3(x8, x9) -> f6(x8, x9) :|: x8 <= 1
4.69/1.99	Start term: f1(i, n)
4.69/1.99	
4.69/1.99	----------------------------------------
4.69/1.99	
4.69/1.99	(3) TerminationGraphProcessor (SOUND)
4.69/1.99	Constructed the termination graph and obtained one non-trivial SCC.
4.69/1.99	
4.69/1.99	----------------------------------------
4.69/1.99	
4.69/1.99	(4)
4.69/1.99	Obligation:
4.69/1.99	Rules:
4.69/1.99	f3(x4, x5) -> f4(x4, x5) :|: x4 > 1
4.69/1.99	f5(x6, x7) -> f3(x6, x7) :|: TRUE
4.69/1.99	f4(x10, x11) -> f5(x12, x11) :|: TRUE && x12 = x10 - 1
4.69/1.99	
4.69/1.99	----------------------------------------
4.69/1.99	
4.69/1.99	(5) IntTRSCompressionProof (EQUIVALENT)
4.69/1.99	Compressed rules.
4.69/1.99	----------------------------------------
4.69/1.99	
4.69/1.99	(6)
4.69/1.99	Obligation:
4.69/1.99	Rules:
4.69/1.99	f5(x6:0, x7:0) -> f5(x6:0 - 1, x7:0) :|: x6:0 > 1
4.69/1.99	
4.69/1.99	----------------------------------------
4.69/1.99	
4.69/1.99	(7) IntTRSUnneededArgumentFilterProof (EQUIVALENT)
4.69/1.99	Some arguments are removed because they cannot influence termination. We removed arguments according to the following replacements:
4.69/1.99	
4.69/1.99	   f5(x1, x2) -> f5(x1)
4.69/1.99	
4.69/1.99	----------------------------------------
4.69/1.99	
4.69/1.99	(8)
4.69/1.99	Obligation:
4.69/1.99	Rules:
4.69/1.99	f5(x6:0) -> f5(x6:0 - 1) :|: x6:0 > 1
4.69/1.99	
4.69/1.99	----------------------------------------
4.69/1.99	
4.69/1.99	(9) PolynomialOrderProcessor (EQUIVALENT)
4.69/1.99	Found the following polynomial interpretation:
4.69/1.99	[f5(x)] = x
4.69/1.99	
4.69/1.99	The following rules are decreasing:
4.69/1.99	f5(x6:0) -> f5(x6:0 - 1) :|: x6:0 > 1
4.69/1.99	The following rules are bounded:
4.69/1.99	f5(x6:0) -> f5(x6:0 - 1) :|: x6:0 > 1
4.69/1.99	
4.69/1.99	----------------------------------------
4.69/1.99	
4.69/1.99	(10)
4.69/1.99	YES
4.72/2.06	EOF